Efficient stretching of DNA in microfluidic devices is important for new genomic mapping methods such as with Direct Linear Analysis. Two aspects of these devices that are common are the transient nature of the stretching and a change of the strain rate over the scale of the molecule. We have investigated the stretching of DNA undergoing electrophoresis across a step change in mobility, which is a simplified system which has these two properties. This system represents a limiting regime of experiments and allows us to use a toy model to identify the key dimensionless groups, an effective Weissenberg number and Deborah number. Using the toy model we determined the scaling of the stretch with those groups and verified the results using Brownian dynamics simulations. Key features of the stretching are that there is no coil-stretch transition and the finite extensibility only affects the response if the chain is stretched to a significant fraction of the contour length.